Median is an average, as is mean and mode. Saying median not the average makes no sense. You mean median not the mean. All three are different kinds of averages.

I never realized that the median is an average... interesting. So any average can be dominated by extreme events, except the median average.

Then we are discussing averages, in general. So, the common misconception would be:

-Averages are dominated by the median, and deviation from the mean is symmetric.-

> This is a common misunderstanding, but actually 50% will do better than the median not the average.

If the market were skewed to the degree that a symmetrical normal distribution wasn't a realistic model, then (assuming a particular skew) beating the median would be child's play, but it also wouldn't produce returns different than the average portfolio -- that average portfolio that sits at or near the mean, not the median.

Another way to say this is that, if a skewed distribution peaked at some mean value M (the value on the curve that has a zero first derivative), and if there was a pathological, nonsymmetrical tail at the right or left that shifted the median value, the majority of portfolios would remain at the mean value in spite of the asymmetry.